Mixed response of trace element concentrations in fluvial sediments to a flash flood in a former mining area

Background Floods, especially flash floods, are the major transporting agent for fluvial sediments, whose pollution is a global concern. As floods result in the dispersion of and exposure to these sediments, a profound understanding of sedimentary dynamics during flood events and the related pollutant dispersion is of relevance. However, the characteristics of extreme flood events concerning pollutant dynamics are insufficiently known so far. Results In a Central European catchment impacted by intense industrial activities and former mining, over the course of five years, we surveyed six high-discharge events, five of them approx. bankfull discharge and one major flash flood event, supplemented by sampling of bank sediments. Fluvial sediments were analyzed for elemental composition by X-Ray fluorescence and for grain size distribution of the fine faction by laser diffraction. By applying a local enrichment factor, trace metal(loid) signatures in these sample sets were compared. Furthermore, Positive Matrix Factorization was used to investigate the trace metal(loid)s’ sources. The sediments deposited by minor flooding had continual trace metal(loid) signatures. However, for the extreme event, significant divergencies arose and persisted for the following years: The enrichment of anthropogenically influenced elements increased, with a slowly decreasing trend in the subsequent two years. Naturally dominated metal(oid)s decrease in enrichment without indicating a return to original levels. In contrast, other elements were insensitive to the extreme event. Positive Matrix Factorization identified anthropogenic influences in elements originating from copper and lead processing and mining activities. Furthermore, bed sediments and a natural background factor were found to dominate the non-anthropogenically influenced metal(loid)s. Conclusions In between extreme events, winnowing processes slowly alter the elemental composition of bed sediments. The depletion of such sediments due to the flash flood proves catchment-wide flushing, which induces a natural resetting of the geochemical signals. This ability to renew is an integral part of resilience in fluvial systems. This mechanism is disturbed by industrial activities in floodplains. The exceptional flooding reaches infrastructure that is assumed to be safe and, therefore, unprotected. These additional sources can shift flood sediments’ trace metal(loid) signature, which has a long-lasting impact on the catchment sediments. However, the modifications depend on the flooding extent, possible emitters, and protection measures.

Since more than 90% of trace metal(loid)s are transported as particulate matter [14,15], sediments must be addressed to understand the dynamics and the fate of trace metal(loid)s [16].Flood events can induce vigorous sediment mobilization in relatively short periods [17,18].Notwithstanding the prognosis of rising frequencies and magnitudes of flood events due to climate change [19,20], a growing part of the human population lives in flood-prone areas [21][22][23][24].Yet, despite being relevant to millions of people, the risks arising from flood sediments are often neglected [25].
No simple, straightforward correlation exists between trace element1 concentration and discharge or sediment load [26][27][28][29][30].In the first stages of flooding, i.e., during the rising limb, unconsolidated fine sediments get eroded, leading to quickly rising concentrations of suspended sediments that reflect the contamination status of bed and channel sediments [14].However, they are mostly washed out of the catchment, as floodplain deposition occurs during receding waters [14].During the following stages, the situation depends on the sediments eroded: while some studies report high discharges leading to intensified input of pollutants into the fluvial system (e.g., by erosion of pollution sinks) and, in turn, to enhanced concentrations of contaminants in flood sediments [4,14,15,[31][32][33][34], others provide evidence for the limited influence of flooding on pollutant levels [35,36] or even decreasing of pollutant concentration due to flushing of the catchment [37,38] or suggest dilution with 'clean' sediments [26,30,[39][40][41][42]. Depending on the pollution intensity and distribution within the catchment, there is a variable discharge threshold above which additional pollutant sources outweigh the dilution effect [43].On the other hand, flooding can induce the exhaustion of pollution sources.A further influence on the trace element concentrations arises from the area of deposition [30,43].Hence, the impact of extreme flood events on the dynamics of sediment-bound pollution is highly catchment-specific and depends on the initial state of the catchment's sediments prior to the flooding.
In this study, we attempt to improve the understanding of how extreme flash flood events differ from regular flooding events regarding trace element dynamics.To this end, we compare trace element enrichment in flood sediments of flood events of differing magnitude in a Central European catchment severely impacted by historical mining and industrial activities.FA employing PMF provides further insight into the sources of trace elements and sediment dynamics.This approach combines the rather 'traditional' method of enrichment assessment with a robust statistical analysis.
Thereby, we address the following hypothesis: 1.The trace element signature in fluvial deposits is discharge-dependent.This implies similar geochemical profiles for regularly reoccurring high-discharge events (bankfull discharge or events that induce minor flooding of the floodplains at most) and deviations from that trace element inventory for extreme events.We assume these divergences to be elementdependent.
2. The impact of the extreme event on the channel sediment's geochemistry is longer-lasting.3. PMF is a suitable tool for investigating complex sedimentary systems affected by an unknown number of emission sources with not entirely homogenous emission profiles.

Study area-the Inde catchment
The Inde River catchment, 344 km 2 in area, is located in western Europe in Belgium and Germany.The perennial river's source is in the medium-range mountains of the northern Eifel.After 30 km, it enters the Lower Rhine Embayment before watering into the Rur River (Fig. 1, map A).The most relevant tributary is the Vichtbach.At the most downstream gauging station (20 km upstream of the river's mouth), the Inde has a mean discharge of 2.77 m 3 /s, and the mean discharge during yearly reoccurring flood events is 46.57m 3 /s [90].All-year precipitation has a slight maximum in the summer months when intense precipitation events can lead to flood events with steep flood waves, as in summer 2021 (see next section).However, flood events in the winter months are more common due to snow melting in the Eifel mountains [91].
From Stolberg downstream, the Inde and Vichtbach have fully anthropogenically constructed bank structures.They were built in the 1970s as an extensive flooding protection.Ever since then, even the discharge of an event with a reoccurrence interval of 100 years induces only locally limited overflowing of the floodplains.
On its relatively short course of 54 km, the Inde crosses the border from the mid-mountain ridge to the lower Rhine embayment.This results in strongly differing conditions regarding valley shape (from v-shaped to very flat and wide valleys), gradient of the river (from steep to relatively flat), and underlying geology: in the Eifel mountains, the Inde crosses Cambrian to Devonian sedimentary lithologies that are widely covered by periglacial cover beds, and Carboniferous limestones with economically relevant ore deposits.In the lowlands, the catchment is underlain by Quaternary sediments (mainly loess) (Fig. 1, map B).The Vichtbach, on the contrary, entirely flows in the mountainous area.It is very steep, with quick-flowing flood waves.In the upper reaches, there are, in many places, no extended floodplains.Instead, the valleys are v-shaped, and the steep slopes do not allow for the development of sedimentary floodplains.
The Inde catchment was intensely shaped by the mining of hard coal, iron, lead, and zinc ores [92][93][94].In addition to the ores, the region was rich in wood for charcoal production and creeks suitable for hydropower usage.This availability of resources led to the establishment of various industries along the streams of the catchment.From the 16th to the beginning of the 20th century, the city of Stolberg, located at the confluence of the Vichtbach and the Inde, became a supra-regional center of the brass and, later on, the glass industry [94,95].Many of these industries influenced the river by discharging wastewater directly into the river.In addition, the landfilling of waste material on the company's private land, which was little regulated then, has resulted in an almost unmanageable number of brownfield sites, many located in the floodplain.Furthermore, atmospheric emission of metal-bearing dust induced a widespread enrichment of, among others, Pb and Cd [96].Detailed information on the Inde catchment and its industrial legacy can be found in Esser et al. [93] and references therein.Today, only a few large-scale industrial units are left.Many of them are located along the Vichtbach in Stolberg, forming a cluster of metalworking industries.

The July 2021 flooding
From July 14th to July 15th, 2021, the Inde catchment was affected by intense rainfall, leading to an extreme flood event.An estimated doubled monthly average of precipitation fell within these two days over large areas of the German-Belgian Eifel-Ardennes, causing severe flooding in most rivers draining the low mountain range (Fig. 2) [97][98][99].Many stations recorded their all-time maximum of precipitation within 24 h [100], and overall maxima reached > 150 mm within one day [101].As this excessive rain, with locally occurring torrential rain, fell on short, steep valleys, it induced a flooding crisis affecting parts of western Germany, Belgium, Luxemburg, France, and the Netherlands [102].Waterlogged soils aggravated the situation: prior to the days with extreme precipitation, prolonged rainfall of lower intensity caused almost completely water-saturated sediments, thereby inducing quickly flowing surface runoff [101,103,104].This surface flow led to a rapid rise of water levels in the receiving rivers and exceptionally intense erosion along channels and on surfaces [105].The event is a textbook case of a flash flood with quickly rising water levels, extremely short response times, high flow velocities and transport capacities, and consequential intense erosion [106].Extensive descriptions of the event can be found in Dietze et al. [104], Mohr et al. [102], Ludwig et al. [107], and Lehmkuhl et al. [98].
In the immediate aftermath of the flooding, when the extensive deposition of flood sediments became apparent, concerns arose due to the possible contamination of the sediments [108].The exceptionally high water levels caused overflowing in areas usually unaffected by flooding, which activated additional pollution sources, as shown by enhanced pollutant levels in the exceptionally widespread deposited sediments [109,110].

Sampling
In the aftermath of six different high-discharge events (April 2018, June 2018, January 2019, March 2019, July 2021, and February 2022), freshly deposited fluvial sediments were collected.All sampling points are depicted in Fig. 3.The fine-grained material was scratched from vegetated or, if the flooding extent reached settlement areas, sealed surfaces like pavements or asphalt and stored in Whirl Pacs until further analysis.Details on the six Fig. 1 General map (A) of the Inde River catchment with its main tributaries, Vichtbach and Wehebach, and a geologic map (B) of the catchment.The most downstream part of the Inde was relocated in 2007 due to the progression of an open-pit lignite mine.The relocated reach is named "Neue Inde" (translates to "New Inde").The settlement and industrial center is around the towns of Stolberg and Eschweiler, where the center of the ore mining and processing industries was located events and the sampling locations are given in the supplement.Four of the six events were < HQ 5 (HQ 5 describes an event with a reoccurrence probability once every 5 years), which entails bankfull discharge and, occasionally, minor flooding of the proximal floodplain.In March 2019, the HQ 5 threshold was exceeded at some gauging stations.By far, the most intense event was the flood in July 2021, which has already been described in detail.The extremely high water levels led to the widespread deposition of fine flood sediments [110].
In addition, in March 2022 and July 2023, bank material was sampled to provide further insight into the trend of trace element enrichment in the fluvial sediments in the aftermath of the extreme event in July 2021.Bank sediments are of particular relevance for trace element assessment because of the rapid cycling of these sediments and the exposure to bioturbation, water movement in the hyporheic zone, and changes in redox state, all contributing to a potential increase of the bioavailability of possible risk elements [111,112].The specific geomorphologic situations were considered, and we carefully selected sampling spots where deposition of sediments at slightly elevated discharge is expected.This sediment can be seen as part of the throughput load and is a recommended endpoint for assessing river pollution [113].Samples were collected by using a spade to extract cubes with an edge length of 20 cm.These cubes were sampled evenly along the 20 cm depth.If the lower limit of the sediments of the July 2021 flood was clearly recognizable, the sampling was limited to these sediments.However, this was the exception, probably because, in most sampling locations, more sediment was deposited during the 2021 extreme flood.
Furthermore, to gain insight into the anthropogenic enrichment of trace elements with respect to their geogenic background, we sampled topsoils in the floodplains of the upper Inde catchment in places where anthropogenic influence is minimal (see Figs. 1 and 3).The sampling was limited to siliclastic lithologies, even though smaller parts of the catchment are underlain by calcareous bedrock.As the area of outcropping carbonates is small and intensely anthropogenically influenced, it is unsuitable for any baseline sampling.Eighteen samples were collected along the upper Inde River itself.Here, Fig. 2 The catchments most affected by the July 2021 flood event.Rainfall data is based on REGNIE hourly precipitation data, which is only available for Germany.The highest rainfall intensities (right map) coincide with areas with upstream midrange mountain areas with short, steep valleys (left map).This combination led to an unexpectedly quick rise in water levels, resulting in a devastating flash flood Fig. 3 Overview map of the nine sampling campaigns conducted in the Inde catchment from 2018 to 2023.In addition, the number of samples and the objective of each campaign are given.The color scheme will be applied in all further figures differentiating the sample sets the Inde flows in a fairly natural environment within an inhabited protected landscape with sporadic forestry use.The "Weißer Wehebach", a tributary of the Wehebach, which flows into the Inde (see Fig. 1), is classified as the river with the most natural condition within the Inde River Basin.Therefore, another set of topsoil samples was collected in its floodplains.The sampling technique was identical to the bank samplings.

Laboratory analysis
Samples were dried at 35 °C and larger organic particles were removed by hand before being carefully ground using an agate mortar and sieved to < 2 mm.For the analysis of elemental concentrations, the remainder of the samples was fully dried at 105 °C for 12 h.8 g of the sediment were mixed with 2 g Fluxana Cereox binder, homogenized by shaking, and pressed to a pellet by applying a pressure of 19.2 MPa for 120 s.Energy-dispersive polarized X-Ray fluorescence (XRF) (Spectro Xepos) measured elemental compositions in duplicate with rotation of the pellet in between measurements, and the arithmetic means were used for further analysis [114], which focused on Ti, V, Cr, Co, Ni, Cu, Zn, Ga, As, Rb, Sr, Y, Zr, Nb, Cd, Sn, Sb, Ba, Nd, Hf, Pb, and Th.Measurements were calibrated using certified reference materials of soils (CRM No. 5360-90, CRM No. 5358-90, CRM No. 2499-83, CRM 2505-83, CRM 2508-83, CRM No. 5359-90, SARM 42, USGS GXR-2, GXR-5, and GXR-6).All XRF measurement results, their root mean errors, and the element's detection limits are provided in an Excel spreadsheet as part of the supplementary material.
To assess grain size distribution, the organic material was removed by treating the sediment repeatedly with 0.70 mL 30% H 2 O 2 at 70 °C for several hours until the material bleached.Samples were also treated with 1.25 mL Na 4 P 2 O 7 (0.1 mol * L −1 ) overnight with an overhead shaker to ensure the dispersion of particles [115,116].Laser diffraction measurements were performed using a Beckman Coulter LS 13 320.The resulting 116 particle size classes indicate the percent size frequency of particles from 0.04 to 2000 μm with an error of 2%.Particle size distribution was calculated using the Mie theory (Fluid RI: 1.33; Sample RI: 1.55; Imaginary RI: 0.1) [117][118][119].

Calculation of a local geochemical baseline and a local enrichment factor
Among the many factors determining the trace element concentrations in sediments are the geologic source region, the content of organic material and Fe-Mn oxides, and sediment sorting [49,[120][121][122][123].Therefore, any assessment of enrichment of trace elements needs to be done based on a reference level to investigate deviations from these expected concentrations.Only such a baseline allows for distinguishing anthropogenic influences from natural concentrations.However, as a precise definition of this level on a local scale is often unavailable, many authors rely on global means, such as the elemental composition of the upper continental crust.While this might be suitable for large-scale studies, it is only of limited use for locally limited sampling sets.Even more so if the sampling area is dominated by anomalies, such as the occurrence of specific ores.Moreover, a background concentration must be based on maximum homogeneity [124].Hence, it should be calculated for a specific environmental compartment [123].Therefore, mean concentrations calculated for rock material are not ideal for evaluating weathered fluvial sediments.
Matschullat et al. [124] define the background as the naturally occurring concentration range of any trace element in anthropogenically non-influenced samples.However, as the Inde catchment is densely populated, a ubiquitous anthropogenic influence has to be assumed (e.g., by atmospheric deposition), which cannot be excluded by any sampling strategy.Therefore, we use the term baseline and define this as the upper limit of the naturally occurring concentration plus the ubiquitous anthropogenically induced enhancement of trace elements, following the definition by Salminen & Gregorauskien [125].
Baseline levels were calculated using the iterative 2σ-approach (described in great detail in [124]), a method suitable for right-skewed distributions [124].It was shown to provide meaningful results specifically for the Inde catchment [91].A sometimes criticized drawback of this approach is its limited applicability if a larger number of outliers is included in the dataset [47,126].However, as the 47 samples used as input for the calculation were collected in the less anthropogenically impacted upper catchment (Fig. 3) from comparable sediment types, no strong influence of actual outliers is expected.Moreover, relying on the mean + 2σ-method provides a high upper threshold of naturally occurring concentrations [126].This, in turn, results in more conservative estimates of the anthropogenic influence.
One of the widely acknowledged difficulties in assessing flood sediment chemistry is the grain size dependence of many trace elements that are preferably found in finer sediments [14,46,127].Hence, the grain size sorting inherent in flood sediments inevitably influences the trace element concentration [17], making correcting for textural biases imperative to compare different locations and events.
To this end, a local enrichment factor (EF) based on the baseline sample set [128] was calculated as where c(TE) is the concentration of the trace element investigated in a specific sample or the calculated baseline, respectively, and c(Ref ) denotes the concentration of a reference element.This reference element, which should function as an indicator for the above-mentioned natural variations in concentrations, needs to be grain size sensitive, free of anthropogenic impact, and conservative within sediments, i.e., not prone to translocation processes [46,47].
As Matys Grygar [129] pointed out, the usefulness of any selected reference element to predict the element of interest's behavior has to be thoroughly checked.Some widely used grain size indicators were plotted against grain size parameters, and a robust regression was calculated to test their grain size dependence (Fig. 4 and Of the six proxies tested, only Al provided acceptable results with a r 2 = 0.3.Hence, as a next step, we checked the covariance of Al and the defined elements of interest in the baseline samples (Fig. 5).We found acceptable correlations for some elements (like Ti, V, Cr, Cu, Zn, Ga, Rb, Sr, Y, Nb, Ba, Nd, and Th).However, for other elements, no correlation with Al was found.This applies mainly to elements known to be anthropogenically influenced, like Ni, As, Cd, Sn, Sb, and Pb, but also Zr and Hf.Regarding the former, atmospheric deposition might play a role: atmospheric input of trace metals was documented even for remote areas of Germany [130] and was a major problem for the area of Stolberg in the 1980s due to the intense industrial activities [96].Therefore, even though the calculation of baseline concentrations based on regressions, as described in detail by Matys Grygar and Popelka [47], is recommended, we opted to calculate an upper threshold as the baseline.This baseline includes ubiquitous enrichment Elements known for some level of ubiquitous anthropogenic influence (such as Pb, As, or Sn) exhibit some scatter.However, elements with limited anthropogenic impact (like Cr, Ga, Ba, or Th) do not deviate markedly from an interrelation with Al.Therefore, we conclude that Al is a suitable element to cover the natural variability of trace elements due to atmospheric deposition and, again, provides rather conservative estimates of the anthropogenic input into the sedimentary system due to fluvial processes.Despite the minor correlations with possibly anthropogenically influenced trace elements, Al was chosen as a conservative reference element because of its clear correlation with elements like Rb or Th, which are usually not anthropogenically influenced, and its ability to serve as a grain size proxy.

Testing for differences in sample sets
The Shapiro-Wilks test was used to test for a standard normal distribution [131] of all subsample sets (i.e., for the 8 events and 22 elements, resulting in 176 subsets).
As the majority of the sets were not normally distributed, non-parametric statistics were used to compare the datasets.Using the Kruskal-Wallis test (KW-test), the 8 subsets of each element's enrichment were compared to each other to gather information on the difference between datasets and, hence, the influence of the flash flood on trace element enrichment in the fluvial sediments.

Positive matrix factorization
The basic idea of FA is a bilinear model: with X being a matrix of observations with m samples and n measured properties for each sample [132].This matrix can be factorized into two smaller matrices, G and F, often labeled as scores and loadings.E denotes the error, i.e., the variation in the input data not covered by the product of G and F. Based on this equation, the residual matrix can be denoted as where p symbolizes the selected rank of the model, i.e., the number of modeled factors.PMF, as introduced by Paatero and Tapper [66], aims to solve the factor analytical problem by applying a weighted least squares approach.Under the constraint of non-negativity, the object function Q (Eq.4) is iteratively minimized.
Here, the residuals E are weighted with the data point-specific error estimation σ, called uncertainty [88].The resulting Q is often referred to as Q true [58].This approach makes ideal use of data characteristics in (2) physical sciences, where experimental uncertainties are usually available, and accuracies within columns and rows are unsteady [133].Thus, potential outliers and the typical right-skewed distributions, which are an integral part of environmental analysis [66], can be included in the modeling process [134].Furthermore, missing data and data below the detection limit can effectively be included in the analysis by enhancing the uncertainty of respective data points [70,82].
PMF can be applied in robust mode to further limit the influence of extreme values.The resulting Q robust is defined as: which limits the outlier distance incorporated into the minimization process to α [58].A commonly applied value is α = 4.
The uncertainty calculation is a crucial step in PMF modeling [66].The approach, including the handling of missing values and concentrations below the detection limit, as established by Pollissar et al. [70], is used in the majority of PMF publications [58].It takes into account the detection limit and the analytical uncertainty.However, there is no linear relationship between analytical error and measured concentration for most compounds analyzed in this study.Moreover, their distributions are mostly right-skewed.Therefore, introducing an additional parameter accounting for the concentration value itself was necessary.By doing so, the uncertainty of highconcentration values is dominated by their concentration, so possible outliers are downscaled.On the other hand, the uncertainty of small-concentration data points is dominated by the detection limit and measurement uncertainty [135].Hence, for uncertainty calculation, a combination of the approaches by Polissar [70] and Vaccaro [82] was applied: (5) with u ij being the analytical uncertainty of the j th element in the i th measurement, dl j the detection limit of the j th element, and x ij representing the measured concentration of the j th element in the i th sample.The element-specific factor d j is a proportional coefficient, as proposed by Vaccaro et al. [82] for the PMF analysis of XRF-measured concentrations of trace elements.For elements not covered by their approach, d j = 0.15 was assumed.For Cd, Sn, and Sb that have low abundance, d j was set to 0.25.Even though this is somewhat arbitrary, it seems reasonable as it is within the range of the established d j values, and Vaccaro et al. [82] showed that changing the coefficients by a factor of 2 does not significantly influence the resulting factor structure.Details are provided in Table .S3. Included elements were limited to trace metal(oid)s with a signal-to-noise ratio (S/N) of S/N > 2 (calculated following [89]).Exceptions were made for Cd (S/N = 1) and Sb (S/N = 0.9) because they are relevant pollutants in the Inde catchment [110,136].To account for their low S/N, their uncertainty was tripled [89].In addition, Co was excluded because it induced difficulties in the modeling process (i.e., by quickly generating a factor purely dominated by this element).In summary, the following elements were included in the PMF model: Ti, V, Cr, Ni, Cu, Zn, Ga, As, Rb, Sr, Y, Zr, Nb, Cd, Sn, Sb, Ba, Nd, Hf, Pb, and Th.For details on the settings, see Table S2.PMF calculation was done using EPA PMF 5.0.
One of the critical steps in modeling using PMF is deciding on the number of factors that offer an ideal representation of the observed data without overfitting the model to the data's inherent noise [64].Solutions with 2 to 8 factors were tested.Table 1 displays a detailed comparison of the respective results.For details on the parameters mentioned in the following passage, the reader is referred to publications focusing on the methodological aspects of PMF [58,67,89,[137][138][139].
For a start, the investigation of the Q values is helpful.A ratio of Q true /Q robust = 1 would imply a model not influenced by any outliers.However, this might only be reached when the model is overfitted.Up to five factors, the ratio shows a significant decrease for each factor added, whereas adding a sixth factor leads to only minor improvements in the ratio (Table 1).Moreover, the fivefactor solution is the first one with all species below the threshold of Q/Q expected < 6, that Brown et al. [137] suggested.Q true and Q robust values were stable for the 100 model runs conducted.For an ideal model, the object function Q approximates the degrees of freedom, defined as with p denoting the number of factors and m and n defining the size of the input matrix, but only accounting for non-weak entries [89,139].Q/Q expected < 1 implies overfitting; hence, five factors are the largest amount of factors possible with overfitting (see Table 1).
Bootstrapping-displacement (BS-DISP) is computationally expensive, especially for large datasets [137], so it was conducted only to check the final solution.The selected five-factor solution provided excellent results: no drops of Q, no swaps in best fit, no swaps in the DISP phase, and no factor swaps for any dQ max levels.The results of BS-DISP are deemed especially meaningful since they include the effects of random errors as well as rotational ambiguity [89,137].As rotations using the (8) F-Peak tool did not clearly improve the model, based on inspection of changes in G-space plots [138,140], no rotation was applied to the final model.The selected five-factor model is generally of high quality and performed best in the bootstrapping (BS) and displacement (DISP) analysis among the tested solutions (Table 1).Four of the five factors were remodeled in 100% of the 100 BS runs.The only mismatched run was found for the Cu-dominated factor, which, in many samples, has no contribution.The DISP analysis resulted in no drops of Q and no factor swaps.Adding a sixth factor leads to splitting the factor dominated by Cu and Sn into two factors (Fig. S6 in the supplement), each representing mainly the variance of each species.However, they exhibit strong co-occurrence (with a correlation of r = 0.6, p < 0.001).Therefore, modeling them into one factor seems reasonable.
Looking into element-specific errors, some compounds have higher errors (Fig. 6).However, for all elements used for factor identification (factor 1: Zr, Hf; factor 2: Cu, factor 3: Sb, Pb; factor 4: V, Rb; factor 5: Zn, Cd, Pb, As, for details see results chapter), only minor errors were found in BS, DISP, and BS-DISP analysis in the respective factors.In addition, they all have a reasonably high coefficient of determination (r 2 > 0.7) between observed and predicted concentrations (see Tab. S3 in the supplement) except for Hf (r 2 = 0.49) and Sb (r 2 = 0.69).Cr, Sr, Ba, and Nd have lower r 2 (0.4), but no factor's identification relies on these elements.

Comparison of the geochemical signatures of the flood sediments
For the four flood events from 2018 to 2019 (all ≤ HQ 5 ), a very uniform pattern was found: the four events exhibit similar geochemical fingerprints with only a few exceptions, that are limited to elements with a generally low EF (Nd 04/ 18 All results from the subset analysis are depicted in Fig. 7. When looking at all datasets (including the extreme events and the samples taken during the following years), no uniform trend can be identified for all trace elements.Instead, there are groups of elements for which a typical behavior can be determined.A clear differentiation between elements indicating supply through human activities and rather natural elements is evident, which were merged into Groups A and B, respectively.Based on the differences in enrichment between different events, the two groups were further divided into subgroups (A.1, A.2, A.3, B.1, and B.2).
Pb, Cd, Cu, As, and Zn form Group A.1.The flash flood led to a marked increase in enrichment for these elements.In the aftermath of the extreme event, there is a decrease in enrichment with different rates of change between the elements.According to the KW-tests, two years after the flash flood, the enrichment factors of these elements are comparable to the situation before the extreme event.However, the boxplots exhibit a pronounced upper tail of the distributions, pointing at a general downward trend but with several sampling points still strongly affected by the intense input of these elements during the flash flood.The influence of the topmost quartile of enrichment values is apparent for Zn: the KW-tests reveal almost no differences between events.However, inspection of the boxplots shows much higher enrichments since the extreme event, even though they seem locally limited.Group A.2 is characterized by a substantial increase of EF only during the extreme event.All events before and after exhibit the identical distribution of low EF.This singular peak implies the influence of a source that only gets activated during extreme events.This group solely comprises Sb.The elements in Group A.3, namely Sn and Ni, have similar enrichments for all events according to the KW-tests, implying no influence of the extreme event.Nevertheless, in some samples, the EF is > > 1, indicating that these elements are exceeding the baseline, hinting at an anthropogenic source that seems active independently of flood events.Consequently, there is no detectable degradation trend in the years after the flash flood.
Group B.1, consisting of Co, Cr, Zr, Y, Ti, Nd, Nb, Hf, and Th, responds with a downward level shifting to the flash flood.For the four events prior to 2021, the enrichments are on a fairly stable level.However, enrichments dropped markedly from the extreme event onward and are now closer to EF = 1.Enrichments stayed consistently at the new low level for Co, Cr, Zr, and Y.For Nb, Hf, and Th, slightly lower enrichments are found for the 2023 sample collective.The elements of Group B.2, Rb, Ba, Sr, Ga, and V, have a low enrichment in common, but no clear distinction for before and after the extreme flood event can be identified.A slight downward trend is found for some elements (Sr, Rb, and Ba), whereas other elements (Ga and V) do not show any trends.According to the KW-test, there are some differences between the populations, but as the enrichments fluctuate around 1, these are assumed to represent natural variances.The assumption that these elements are influenced mainly by natural processes is further supported by their small concentration ranges [57,141] and the low skewness of their EF distributions, as can be seen from the boxplots (Fig. 7).For elements that factor identification is based on, observed and modeled concentrations are in good agreement Fig. 7 Notched boxplots of the trace elements' EF (y-axis) for the eight sample sets.For each element, the results of the KW-tests are given in the table below the plot, with darker red indicating a significant difference on the 0.05 significance level and bright red indicating no significant difference between the two populations.The elements are grouped based on concentration trends.For a detailed explanation, see the text.Sequel of Fig. 7.For an explanation of symbology, see Fig. 7, part 1

Factor identification
Factors 3 to 5 are dominated by elements primarily associated with anthropogenic emissions [65,85,[142][143][144], whereas factors 1 and 2 are dominated by elements occurring rather naturally in sediments (Fig. 8) [85,142,145].This classification is supported by factors 3 to 5 exhibiting a wide range of normalized factor contributions over all samples, while factors 1 and 2 are within a limited range and do not exhibit pronounced fluctuations but relatively steady behavior (Figs.10,11), and by the enrichment levels found for these elements (Fig. 7).Factor contributions indicate the contribution of each factor to the total mass by sample.These contributions are normalized to an average of 1 [89].
Factor 1 is dominated by V, Ga, and Rb with 75%, 74%, and 63%, respectively.In addition, Nd, Ba, Ti, Th, Sr, Y, Ni, As, and Nb significantly contribute in the range of 35-50%.Detailed information on the factor profiles is visualized in Fig. 8.The main elements in factor 1 have low enrichment factors of close to 1 (Fig. 7), hinting at naturally occurring sediments as the source for factor 1. V, Ti, Ni, Th, Rb, Y, Nd, and As are often used as markers for naturally occurring sediments [62,65,83,85,141,142,144,[146][147][148][149][150][151].Therefore, factor 1 is interpreted to account for a background signal representing sediments with minor anthropogenic influence.This interpretation is supported by the absence of any apparent trend in this factor, either in different events or along the rivers (Figs.10,11).
Factor 2 is dominated by Hf and Zr, with 94% and 86% of their concentration, respectively, modeled by this factor.Further relevant elements include Nb, Y, Cr, Ti, Nd, Sr, Th, and Ba, with 57%, 47%, 47%, 43%, 39%, 35%, 33%, and 33%, respectively.The most abundant Zr mineral, by far, is zircon.Zircon and further resistant heavy minerals are enriched in stream sediments due to the naturally occurring sorting affecting fluvially transported sediment [152][153][154].As the ionic radii of Zr and Hf are almost identical, the replacement of Zr atoms by Hf atoms in Zr minerals is so common that all Zr minerals contain at least a small amount of Hf [152,155,156].Hence, a strong correlation of their concentrations is expected.To a lesser extent, Zr is substituted by Nb and Y [156,157].Stream sediment is identified to have the highest median concentrations of Hf, Nd, Ti, and Zr among several sediment types [158,159].Zircon, rutile, and tourmaline are the typical heavy minerals enriched in weathered material derived from the Devonian slates in the study region [160][161][162].Therefore, the high contribution of Ti to factor 2 can be linked to rutile, whereas the Cr content might be linked to tourmaline.The Eifel region is known for high Cr concentrations in bed sediments [158].Li et al. [85] found Hf to indicate weathering in their PMF model.
The link between factor 2 and heavy minerals was tested using the winnowing index (WI) proposed by Grunsky et al. [145].In this ratio, Al represents the lightweight clay fraction, whereas Th is supposed to indicate heavy minerals.Hence, a higher WI points toward the depletion of clay minerals and relative enrichment of heavy minerals, for example, due to winnowing processes.The relation between PMF factor 2 and the WI is depicted in Fig. 9. Higher contributions of factor 2 cooccur with an enhanced WI, thereby supporting the relevance of heavy minerals for this factor.However, there are some deviations from this connection for some samples, mainly of the flash flood event.As these samples are characterized by high factor contributions of the anthropogenic factors 3 to 5 (see below for the detailed description of the factors and Fig. S8 in the supplementary material for visualization), the enhanced Th concentrations in these samples might be linked to emissions of the metallurgical industries overflown during the extreme event.Altogether, factor 2 is interpreted to represent bed sediments impacted by hydrodynamic sorting.Detailed visualization and discussion of the impact of hydrodynamic sorting on factor 2 is provided in Fig. S10 in the supplementary material.
The remaining three factors have different characteristics, all containing only a few elements each.For factor 3, these are mainly Cu and Sn, with 68% and 28%, respectively.In addition, Cd, Cr, Ni, and Zn are of minor importance (13%, 12%, 11%, and 11%, respectively).Due to the occurrence of zinc ore in the region, Stolberg became a core area of the European brass industry in the nineteenth century.Some of these businesses have survived to this day and expanded their product palettes.Today, globally operating businesses produce a wide range of metallic products, including brass and bronze alloys with Cr, Zr, and Ni admixtures.Some companies use electroplating techniques, which require large basins in which the substances used, like Cu, Sn, Zn, or Ni, are present in dissolved form.Therefore, factor 3 is interpreted to represent brass industries and other copper processing plants.
Sb, Pb, As, and Sn constitute factor 4, with 70%, 47%, 38%, and 34% of them, respectively, being covered by this factor.Looking into absolute concentrations, lead dominates this factor.These compounds are typically linked to metallurgical industries [148,163,164].The Stolberg region has a long history of lead processing.The emissions of the lead ore processing plants induced severe health issues in the local population, partly due to high lead concentrations in atmospheric dust fall-out [165,166].Interestingly, factor 4 exhibits some variances in the baseline sample set with slightly higher contributions in the Wehebach samples than in the samples taken at the upper Inde River (see Fig. S9 in the supplement).As both sample sets were taken from areas upstream of any industrial or settlement areas, fluvial input of these mainly anthropogenically emitted elements is unlikely.Instead, atmospheric deposition seems probable.As westerly winds dominate in this region, the Wehebach is located downwind from Stolberg, whereas the upper Inde River is in the opposite direction.Therefore, we assume factor 4 represents the lead processing industry, including direct inputs into the fluvial system and reworked atmospheric deposits.
Finally, 75% of Zn, 71% of Cd, and 41% of Pb are accounted for by factor 5. This factor contains smaller Emission-relevant land use in the proximate and distal floodplain is depicted below the x-axis.For details on illustrations, the reader is referred to the legend in Fig. 10 amounts of As, Ni, Cu, and Sn (23%, 22%, 18%, and 17%, respectively).The mining of Zn and Pb ores formerly dominated the region.These ores typically contained accessory amounts of further metals like Ni, Cu, As, Cd, and Sn [136].Cd and Pb were found in several studies to accompany Zn ore mining and processing [81,83,86,149,167].This factor exhibits a distinct "peak area" between the mouth of the Vichtbach and the city of Eschweiler.This area is known for a large number of brownfields.Therefore, factor 5 represents the legacy sediments of the former mining activities and the subsequent processing of the ores.

Spatial patterns of factor contributions
An analysis of the factors' characteristics during the different events and along the Inde and Vichtbach rivers was conducted based on factor contributions.This grouping is visualized in Figs. 10 and 11.Localizing unusual factor contributions can help identify specific emission sources, e.g., metal-processing industrial units, and may support the factors' identification.
The reaches with exceptionally high contributions in factors 3 to 5 coincide with the areas with intense industrial activity on the floodplains for both the Vichtbach and the Inde, thereby backing up the interpretation of these factors as related to anthropogenic emission sources.For both rivers, contributions of the anthropogenic factors are low upstream from the uppermost industrial units in the floodplains.Along the Vichtbach, contributions seem to grow constantly down to the mouth of the river.In the Inde River, the contributions of anthropogenic factors show a first marked increase from the Vichtbach mouth onward.However, even though there are many industrial units in the Inde floodplains in this reach, we found a slow but steady decrease in contributions of anthropogenic factors.When the "Neue Inde" is reached, factor contributions return to levels observed upstream of the industrial hotspots.
The two prominent outliers in the Cu-factor are both found in samples taken at the "Kupfermühlenkamp" which roughly translates to "Copper mill plot", indicating the processing of copper materials.However, the influence of these particles with exceptionally high copper contents is spatially very limited.A similar effect of locally strongly enhanced contributions can be seen for the ore mining factor that peaks at river kilometer (rkm) 7.4 of the Vichtbach (Fig. 11), which coincides with the uppermost former mining activity in the river's surroundings.

Comparing factor contributions in different events
Furthermore, comparing the different events allows for identifying the possible impact of the extreme event in July 2021.The following observations apply to both rivers.For the background factor, no apparent differences related to the extreme event were found.On the contrary, the second "natural factor" had distinctively higher contributions before the extreme event.Since the extreme event, factor contributions have been at a constant, lower level.
For all three "anthropogenic factors", a contrary trend with higher contributions in the aftermath of the event is evident.This does not apply to the upper reaches of Inde and Vichtbach, where contributions are generally low.The only exception is the ore mining factor, which shows a slight increase in the Inde River above the confluence of the Vichtbach since the extreme event.The input of trace elements from the Vichtbach into the Inde River necessarily shapes factor contributions from the confluence downwards.For all three anthropogenic factors, peak contributions for the extreme event and the consecutive data sets are much higher than for the sediments sampled before 2021.Along the Inde River, there is a downward trend in contributions that is especially distinct for the ore mining factor.

Discharge dependency of trace element signatures in flood deposits
More regularly occurring flood events in northwestern European catchments are usually linked to steady rain over several days or snowmelt [19], both inducing slowly rising discharge in rivers.On the contrary, flash floods like the one in July 2021 are induced by extreme precipitation, leading to overland flow and inducing an unusually rapid discharge rise [104].The resulting flood wave is steep, with very high water levels, widespread flooding, and outstanding stream power [106].Therefore, sediment conveyance depends on the type of flooding.Recent studies found flash floods to be very effective transporting agents of suspended particulate matter and associated trace elements [168][169][170].Differences in the trace elements load during extreme discharge events were found in mining-impacted catchments [16,18,171].The particularly effective transport during flash floods also shaped the processes in the Inde catchment in July 2021.
For some elements, a marked drop to EF ≅ 1, i.e., baseline levels, from the flash flood onwards was found.This group (B.1) is dominated by elements that typically become enriched during weathering processes [172].This indicates that the sediments stored within the river bed prior to the flash flooding that were subject to intense weathering were flushed out of the catchment, which hints at the abrogation of the sediment cascade that usually dominates the transport processes of flood sediments in any catchment.Further indication for this is found in the results of the PMF, which confirm the relevance of hydrodynamic sorting effects (for details on this see Fig. S10 in the supplementary material).
The slightly enhanced flow velocities of minor flood events are sufficient to entrain fine bed sediments up to small gravels.However, the transport capacity is not particularly high, so for sand and gravel only short-distance transport occurs, inducing deposition on nearby river banks and floodplains.This effect is evident for the sampled flood events in 2018 and 2019, which have higher contributions of the stream sediment factor.The striking decrease in this factor's contributions at the Inde River for all 2018 and 2019 events is related to changes in the riverbed's structure.From rkm 24 downwards, there is a drop in the roughness of the riverbed, which would be a prerequisite for effective sediment storage [173].The artificial riverbed with minimized micro-scale structures lacks the potential for the retention of particles.Thus, there is a lower level of heavy minerals in the flood sediments (see Fig. 10).This abrupt change also implicates locally limited sediment transport during regular flood events, i.e., the sediment cascade is effective on short distances.Heavy particles tend to be transported via saltation, resulting in short-distance transport [173].
However, this observation does not apply to the flash flood: the contributions of factor 2 drop to a constantly lower level for all river reaches in the aftermath of the event, which points to the catchment-wide flushing of bed sediments.A short flushing effect at the onset of increasing runoff (Fig. 12) is generally acknowledged for all levels of flood events [39,174].This depletion of the stored fine sediments results in a clockwise hysteresis of fine-sediment concentration, typical for mid-European low mountain range rivers [175].Usually, the declining gradient of rivers along their course causes a decrease in their velocity and, hence, their relative transport capacity, resulting in sedimentation in the case of sufficient material supply, thereby minimizing the flushing trend in lower catchments [176].This is not only limited to floodplain deposits but also applies to in-channel sediments [176].However, the minimal contributions of mature sediments along the complete river course since the Fig. 12 Simplified visualization of the findings on sediment dynamics during flash flood events in gravel-dominated rivers.Discharge extremes result in high transport capacities, inducing a clockwise hysteresis of sediment transport.Hence, old channel sediments are completely flushed from the catchment, and flash flood deposits are rather dominated by 'fresh' sediments and anthropogenic impact due to the widespread flooding of unprotected infrastructure in the floodplains flash flood prove that the transport capacity during the extreme event was high enough to impede this process: the entire catchment was affected by such intensive erosion that all the fine sediments (< 2 mm) that were temporarily stored in the riverbed were flushed out.
In arid environments, the flushing effect of flash floods is documented to be so intense that all geochemical signals are reset back to baseline levels, including those influenced by anthropogenic input [170].Siltation of riverbeds deteriorates the permeability of the bed [176], thereby inducing a multiplicity of negative ecological consequences [177].In combination with the 'geochemical resetting' , which implies approaching a more natural level of trace element concentrations, flash floods as a geomorphological process might benefit the riverine ecosystem.
However, this resetting character is disturbed by anthropogenic impact: the peaks of the anthropogenic PMF factors during the extreme event with a subsequent trend of slowly regressing contributions suggest emissions by sources that are solely activated above certain discharge thresholds (Fig. 12) that are not reached during regular flood events.As the Inde catchment is a former industrial hotspot, its floodplains are largely made up of sediments strongly enriched in elements related to these mining and industrial activities [136], and some of these legacy sites eroded during the extreme event [178].The erosion of historically contaminated floodplain sediments is a well-known stressor for fluvial systems [1,16,[179][180][181][182][183][184][185], and flash floods are particularly efficient erosional events [106].Hence, extreme discharge events reactivate legacy sediments through erosion, whereas minor flood events transport present-day pollution [186].The extensive dataset presented in this study supports the concern regarding the ongoing influence of mining legacies on catchments even decades after the last mine closed down [1].Moreover, the overflowing of industrial areas during the extreme event contributed to concentration peaks, as seen from the extreme rise in levels of anthropogenic factors within Stolberg.Here, erosion is limited due to the river being fully channelized with concrete embankments, but industrial units located directly next to the river were hit hard by the flood.
Besides the erosion of contaminated sediments, leaching from water-saturated soils can promote enhanced concentrations of some trace elements in flood sediments [2,16].This effect needs some consideration because flash floods are oftentimes linked to antecedent saturation of soils [106,187,188].Water saturation induces reducing conditions as soon as oxygen available to microorganisms is depleted.Microbial respiration switches to the reduction of iron, simultaneously mobilizing trace elements originally absorbed by this easily reducible iron.
Upon re-oxidation, Fe and Mn-oxides form with a very high sorption capacity for further trace elements [111,172,189,190].Hence, water saturation in sediments can lead to the transport of trace elements from surrounding sediments to the channel, where they re-enter the active fluvial sedimentary system.Ciszewski & Grygar [14] argue that this process is only of minor importance for trace metal transfer from the floodplain to the channel compared to input via eroded bank sediments.However, erosion processes are restricted due to river engineering measures in the lower Inde catchment (i.e., by the trapezoidal cross-section of the river from Stolberg down to the "Neue Inde") [110].Under high antecedent soil moisture, interflow was shown to be of particular relevance during flood events in Central European low mountain ranges [191].In addition, receding water tables induce exfiltration of pore water from the banks [111].Therefore, given the fact that the sorption of trace elements can take place within minutes or hours [111], their leaching from saturated soils seems plausible, but no statements on its relevance are possible.
In exploration geochemistry, it is standard practice to calculate the downstream dilution of a geochemical anomaly, i.e., outcropping ore bodies [120,192].The basic principle behind this idea can be transferred to point source pollution: without further input sources, trace element concentrations will be negatively correlated with the downstream distance from the source [5].Hence, the downward decrease of the anthropogenic factors in the Inde indicates the absence of relevant additional input.Therefore, the onset of the downward trend at the upstream part of Eschweiler (Fig. 13) indicates that settlement areas are only of minor relevance as a source for anthropogenic trace metal(loid) input in the Inde catchment.The remarkably low contributions of anthropogenic factors in the "Neue Inde" are in accordance with other studies on this artificially-built river segment, which is built from uncontaminated, fresh sediment [193][194][195].
Like settlement areas, overflowing wastewater treatment plants were considered concerning pollution emitters.However, we found no proof of their relevance in terms of trace element pollution.Different sources becoming active at specific discharge levels, hence at different times within the event, will influence the respective chemical profile [27] and the spatial distribution of the emitted compounds in deposited sediments [16].For example, compounds emitted by a source active solely in the earliest stages of the event have a high chance of being flushed from the catchment during the following higher stages of discharge.Therefore, the overflowing and flushing of the wastewater treatment plants that occurred early during the event might explain their low contributions to the trace element inventory in the flood deposits.This flushing is in agreement with the results found for the bed sediment factor.
However, the additional input of anthropogenically influenced risk elements during flood events depends on the specific situation of sources within the catchment and is, therefore, also discharge-dependent. High discharge (i.e., discharge events with a return period of > one generation, which strongly limits adaptative capacity) can lead to intense emission of anthropogenic pollution because of widespread flooding and because safety measures are not designed for this discharge level (Fig. 12).The "levee effect" leads to a calamitous sense of security [196] and promotes possibly hazardous land use in floodplains.Flash floods deserve special attention because of their perilous nature [197,198] and because they are a dominating actor in sediment transport [171].The likelihood of significantly enhanced concentrations of possible risk elements in sediments of extreme flood events adds up to these threats and demands a thorough public education on these risks [110].Unfortunately, smaller catchments in rural areas, where oftentimes fewer flood protection measures are installed, are especially affected by flash floods [198].

The long-lasting impact of the extreme event on channel sediments
Differences in the pre-2021 floods, as identified by KWtesting, are limited to trace elements with EF close to 1. Deposits of regularly occurring floods seem to have unvarying trace element composition.For most trace elements, the flash flood disturbed this continuity.The system is expected to return to its old equilibrium state, as seen in the pre-2021 floods (see Fig. 13).However, no predictions on the duration of this can be made.
A clear downward trend was found for those trace elements enriched in the flash flood deposits (Pb, Cd, Cu, As, Zn), leading to the KW-test revealing that their enrichments are back to their respective pre-flash flood levels.This downward trend of anthropogenic factors is also found in the spatial interpolations of PMF factors (Fig. 13).However, the upper EF percentiles are still well above the 'before' values.
Flushing of weathered sediments from the channel was found; it is unclear how long it will take to rebuild the "old" status.Two years after the event, no trend can be observed.The high EF of Hf and Zr before the flash flood point at winnowing over a prolonged period.

PMF is a helpful tool in the analysis of flood sediments
By identifying patterns in trace element concentrations, PMF provided useful insights into flood sediment dynamics.In the vast majority of cases, when used to analyze sediments, only typical 'anthropogenic' heavy metals are used as input for PMF [143,150,199,200].By expanding the suite of trace elements used for the model, in addition to pollution emitters, PMF is also able to single out naturally driven processes like the winnowing of bed sediments.Further research addressing its suitability for provenance analysis in large-scale river systems seems worthwhile.First attempts have already been published [80,85,142,164,201], but the potential of this approach for sediment analysis does not yet appear to have been fully unlocked.
The general differentiation between elements dominated by natural processes and those mainly influenced by anthropogenic activities is found by analyzing enrichment factors corrected for baseline concentrations as well as by PMF (Fig. 14), which uses the original concentration data as input, supplemented by sample-specific uncertainty values.This aligns with other studies that found PMF to successfully differentiate between background factors and several anthropogenic factors [163].The results obtained by the two approaches are in good agreement.However, only PMF, which extracts structural information on the interrelations of elements based on multidimensional data clouds [144], was able to identify differing sources for the anthropogenic elements.In contrast, comparing the distributions of EF is a strictly two-dimensional approach with the corresponding restrictions.Moreover, using PMF, the contribution of single elements to multiple sources (e.g., Pb) can be identified.This differentiation is not possible when relying solely on the EF approach.In addition, PMF showed that Sn and Ni, which were classified as anthropogenic emissions, are not dominated by anthropogenic emissions.Rather, they appear to be part of natural sediment processes to the same extent (Fig. 14).
The modulated uncertainty calculation provided useful results.The results obtained were more stable than when common uncertainty calculation approaches were applied (for a list of commonly used uncertainty approaches, see [58]).As the uncertainty scaling is one of the key features of the PMF, its calculation should be considered duly and dataset-specific since it decides on the model's success [62,66,202,203].
There are several reasons for preferring PMF over other multivariate statistical approaches, such as common FA or principal component analysis (PCA), when dealing with geochemical data.Common FA assumes 'random zero points' (like in social sciences, for example) and normally distributed data [55,133,204]; assumptions that the data presented here do not satisfy.FA and unscaled PCA are unduly influenced by large concentration values, which are a valid phenomenon in environmental sciences [66,133].Nevertheless, log transformations are an often followed approach to achieve normal distributions and limit the influence of high values.However, this destroys the model's linear structure while generating arbitrary power laws and can lead to spurious factors [133].PCA (Q-mode and R-mode) was shown to be based on unrealistic error assumptions for the input data matrix when used in fields such as physics and chemistry [133,140].For both approaches, data transformations are necessary.However, centering the data is not advisable because it will inevitably lead to a loss of information when applied to geochemical data [133].Autoscaling the original data was proven ineffective [134] and induces intensity ambiguity, meaning the solution is scale undetermined [205].Furthermore, the ideal rank of the model depends on the scaling method applied [133].
Instead, PMF offers the unique feature of scaling the input matrix 'element-by-element' [133], ensuring optimal use of the information typically available in environmental sciences, like measurement uncertainties [88].Therefore, no transformation of the input data is needed [73,137,205] so that information loss is avoided (regarding, e.g., the zero point of the data scale) [207].PMF has been shown to provide results better fitting to the input data than FA or PCA approaches [59,60,62,132,206,207].While PCA performs under orthogonal constraints for the generated matrices, which results in solutions without actual physical meaning [132], PMF is based on a non-negativity constraint to enable the calculation of Eq. 2 [66], which leads to more meaningful results when applied in environmental sciences [58,66,73,74,88].
However, a certain level of expertise is required to evaluate the model's result.One frequently addressed drawback of PMF is that the algorithm will almost always provide a solution, leaving the user with the duty to identify misleading or erroneous results even though they might be hard to recognize [67,208].Hence, a thoughtful setup of the model and its parameters, including excessive examination of the results obtained using different model setups, is mandatory.For example, there is ongoing debate on how to determine the ideal number of factors [80].

Conclusions
Sediment deposits from flood events of different magnitudes and bank sediments were sampled over five years to investigate the effect of the discharge level on the trace element concentration in fluvial sediments.
For events with only slightly increased discharge, the transport capacity of the river does not exceed the sediment availability within the channel.Here, a locally limited sediment transport dominates, shaping the wellknown fluvial sediment cascade.This state can be interpreted as a kind of equilibrium that is not disturbed by the aforementioned small flood events.
However, due to their exceptional stream power, flash floods generally induce flushing of the river's fine sediments with the potential to reset the geochemical signal.Such a resetting of the river bed sediments would be ecologically beneficial if the system were not disturbed by the additionally activated anthropogenic emission sources.High water levels, especially when combined with high flow velocities, induce overflowing and erosion in unexpected and, hence, unprotected areas.The material eroded here mixed with freshly eroded sediments from more natural areas forms the flood deposits found when waters receded.Consequently, the enrichment level of anthropogenic trace elements depends on the activated emission sources and, therefore, on the balance between discharge level and flow velocity on the one hand and flood protection measures on the other.However, location and type of sources are the main determining factors.
PMF based on a modified uncertainty calculation provided helpful results for identifying the sources influencing the trace element patterns in the fluvial sediments of the Inde.In addition to natural factors, current and past industrial activities were identified as controlling variables.The frequently expressed concern about emissions from sewage treatment plants and residential areas could not be substantiated for heavy metals in this study.Further investigations on the suitability of PMF for the analysis of sedimentary archives or for provenance analysis seem worthwhile.
In addition, further research is needed to investigate whether there is a direct relationship between transport distance and discharge or whether there is a certain threshold for catchment-wide flushing.Furthermore, the extent to which metals that are dissolved in the interflow and precipitate once they reach the active fluvial sedimentary system participate in elevated trace element levels is insufficiently known.
Fig.S5in the supplement).Of the six proxies tested, only Al provided acceptable results with a r 2 = 0.3.Hence, as a next step, we checked the covariance of Al and the defined elements of interest in the baseline samples (Fig.5).We found acceptable correlations for some elements (like Ti, V, Cr, Cu, Zn, Ga, Rb, Sr, Y, Nb, Ba, Nd, and Th).However, for other elements, no correlation with Al was found.This applies mainly to elements known to be anthropogenically influenced, like Ni, As, Cd, Sn, Sb, and Pb, but also Zr and Hf.Regarding the former, atmospheric deposition might play a role: atmospheric input of trace metals was documented even for remote areas of Germany[130] and was a major problem for the area of Stolberg in the 1980s due to the intense industrial activities[96].Therefore, even though the calculation of baseline concentrations based on regressions, as described in detail by Matys Grygar and Popelka[47], is recommended, we opted to calculate an upper threshold as the baseline.This baseline includes ubiquitous enrichment

Fig. 4 Fig. 5
Fig.4 The six plots depict the relation of the grain size, either given as sum of all grain size classes < 63 µm or as mean grain size, and common geochemical parameters used to approximate grain size characteristics.In addition, the coefficient of determination r 2 is given.For Al 2 O 3 , Fe 2 O 3 , Rb, and Ti, higher concentrations are expected in finer sediments, whereas the SiO content and the ratio of SiO to Al 2 O 3 , should decrease in finer sediments.Based on r 2 , the Al 2 O 3 content is the most suitable approximation of the fine material.Hence, Al was chosen as reference element for geochemical normalization

109 Fig. 6
Fig. 6 Scatter plots of concentrations observed on the x-axes vs. predicted by the PMF model on the y-axes.The red line indicates a linear fit.For elements that factor identification is based on, observed and modeled concentrations are in good agreement

Fig. 8
Fig. 8 Factor composition of the five factors identified by PMF.For details on factor identification, see text

Fig. 9 109 Fig. 10 109 Fig. 11
Fig.9 The plot of factor contributions of PMF factor 2 against the winnowing index reveals a distinct positive relation.This supports the thesis that this PMF factor is formed by density-based sorting processes

Fig. 13
Fig. 13 Spatial interpolation of the five PMF factors for all sample sets.The interpolation was done using the Diffusion Interpolation with Barriers tool in ArcGIS using a DEM with 1 m resolution as a barrier feature.Each band represents a sample set, with the four on the left side of the river representing the 'before' and the four bands on the right side describing the situation since the flash flood.For the high-discharge events in 2018 and 2019, constant patterns are found.The flash flood induced a level change in factor contributions for all five factors

Fig. 14
Fig. 14 Heatmap comparing the results obtained by investigating enrichment factors vs. PMF results.As denoted on the x-axis, the elements are sorted based on the grouping of elements as derived by EF (A-anthropogenically influenced, B-dominated by natural processes).The rows indicate the five PMF factors, and the color scheme visualizes the amount of each element covered by the respective factor.It becomes apparent that the results are similar.However, PMF provides a somewhat deeper and more differentiated understanding